   Chapter 14.1, Problem 78E

Chapter
Section
Textbook Problem

Comparing Different Orders of Integration Using Technology In Exercises 77 and 78, (a) sketch the region of integration, (b) change the order of integration, and (c) use a computer algebra system to show that both orders yield the same value. ∫ 0 2 ∫ 4 − x 2 4 − ( x 2 / 4 ) x y x 2 + y 2 + 1   d y   d x

(a)

To determine

To graph: The region of integration for the given expression.

Explanation

Given:

The expression 024x24x24(xyx2+y2+1)dydx.

Graph:

Take the equations y=4x2,y=4x24,x=0,x=2 into consideration. In order to find and draw the graph of functions, the following Ti-83 steps are used:

Step 1

(b)

To determine
The change in the order of integration

(c)

To determine

To prove: Both orders give the same value using CAS.

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